++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
↳ QTRS
↳ DependencyPairsProof
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
++1(++(x, y), z) → ++1(y, z)
++1(++(x, y), z) → ++1(x, ++(y, z))
++1(.(x, y), z) → ++1(y, z)
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
++1(++(x, y), z) → ++1(y, z)
++1(++(x, y), z) → ++1(x, ++(y, z))
++1(.(x, y), z) → ++1(y, z)
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
++1(.(x, y), z) → ++1(y, z)
Used ordering: Polynomial interpretation [25,35]:
++1(++(x, y), z) → ++1(y, z)
++1(++(x, y), z) → ++1(x, ++(y, z))
The value of delta used in the strict ordering is 1/8.
POL(++1(x1, x2)) = (1/4)x_1
POL(++(x1, x2)) = (4)x_1 + (2)x_2
POL(.(x1, x2)) = 1/2 + (4)x_2
POL(nil) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
++1(++(x, y), z) → ++1(y, z)
++1(++(x, y), z) → ++1(x, ++(y, z))
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
++1(++(x, y), z) → ++1(y, z)
Used ordering: Polynomial interpretation [25,35]:
++1(++(x, y), z) → ++1(x, ++(y, z))
The value of delta used in the strict ordering is 16.
POL(++1(x1, x2)) = (4)x_1 + (4)x_2
POL(++(x1, x2)) = 4 + x_1 + x_2
POL(.(x1, x2)) = x_1
POL(nil) = 0
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
++1(++(x, y), z) → ++1(x, ++(y, z))
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
++1(++(x, y), z) → ++1(x, ++(y, z))
The value of delta used in the strict ordering is 1/16.
POL(++1(x1, x2)) = (1/2)x_1 + (1/4)x_2
POL(++(x1, x2)) = 1/4 + x_1 + x_2
POL(.(x1, x2)) = 0
POL(nil) = 0
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
++(nil, y) → y
++(x, nil) → x
++(.(x, y), z) → .(x, ++(y, z))
++(++(x, y), z) → ++(x, ++(y, z))